Designing Non-monetary Intersection Control Mechanisms for Efficient Selfish Routing

TL;DR

The paper tackles the inefficiency arising from selfish routing in urban networks with autonomous intersections. It introduces a non-monetary mechanism that modulates request timestamps through a two-layer architecture (local RSU scheduling and a central planner) and models driver behavior as a nonatomic routing game with additive path-specific node costs, captured by $c_p(f,u) = \sum_{e\in p} c_e(f_e) + \sum_{v\in p} c_v^p(f_v,u_v^p)$. The core theoretical contribution is that equilibrium flows are the minimizers of the Beckmann-style potential $\Phi(f,u) = \sum_{e\in E} \int_0^{f_e} c_e(x)dx + \sum_{v\in V} \int_0^{f_v} c_v(y)dy + f\cdot u$, with existence and essential uniqueness, enabling a well-defined bilevel optimization where a planner chooses $u$ to minimize $C^o(f(u)) + f(u)\cdot u$ subject to $f(u) \in \arg\min \{\Phi^o(f) + f\cdot u\}$. Experiments on Braess networks and the Sioux Falls network show substantial reductions in the equilibrium-to-optimal gap (up to about 68%), validating the approach's scalability and practical impact without monetary tolls.

Abstract

Urban traffic congestion stems from the misalignment between self-interested routing decisions and socially optimal flows. Intersections, as critical bottlenecks, amplify these inefficiencies because existing control schemes often neglect drivers' strategic behavior. Autonomous intersections, enabled by vehicle-to-infrastructure communication, permit vehicle-level scheduling based on individual requests. Leveraging this fine-grained control, we propose a non-monetary mechanism that strategically adjusts request timestamps-delaying or advancing passage times-to incentivize socially efficient routing. We present a hierarchical architecture separating local scheduling by roadside units from network-wide timestamp adjustments by a central planner. We establish an experimentally validated analytical model, prove the existence and essential uniqueness of equilibrium flows and formulate the planner's problem as an offline bilevel optimization program solvable with standard tools. Experiments on the Sioux Falls network show up to a 68% reduction in the efficiency gap between equilibrium and optimal flows, demonstrating scalability and effectiveness.

Figures (9)

• Figure 1: Autonomous intersection management based on communication between vehicles and RSUs.
• Figure 2: Proposed two-layer solution separating incentive control and local intersection scheduling via timestamp modifications.
• Figure 3: A figurative plot of path costs vs paths under optimal flow $f^*$ without any incentives applied. Vertical arrows depict how incentives can increase or decrease path costs so that optimal flow can become an equilibrium flow, i.e., can satisfy \ref{['eq:equilibrium']}, under incentives while still attaining the optimal cost.
• Figure 4: Comparison of the original (a) three-node/four-edge network and (b) the transformed version with node splitting. The path $p_1=se_1ve_3t$ and its counterpart in the transformed network are highlighted in red.
• Figure 5: A Braess network.

Theorems & Definitions (10)

• Remark 2: Average/Expected Cost
• Definition 3: Wardrop Equilibrium
• Remark 4: Equilibrium Behavior
• Remark 5: Constraints
• Remark 6: Different Intersection Costs
• Example 7
• Proposition 8: Potential Function
• Theorem 9: Existence and Uniqueness
• Claim 10
• Claim 11